Inverse Optimal Stabilization of Dynamical Systems by Wiener Processes

Abstract

Abstract This paper formulates and solves new problems of inverse optimal stabilization and inverse optimal stabilization with gain assignment for nonlinear systems by Wiener processes. First, a theorem is developed to design inverse optimal stabilizers (i.e., covariance matrix multiplied by variance of Wiener processes), where it does not require to solve a Hamilton–Jacobi–Belman equation. Second, another theorem is developed to design inverse optimal stabilizers with gain assignment for nonlinear systems perturbed by both nonvanishing deterministic and stochastic (Wiener processes) disturbances without having to solve a Hamilton–Jacobi–Isaacs equation.